Reset-and-Hold Control of Systems With Time Delay

Abstract

Reset control is a kind of hybrid control which is capable of overcoming fundamental limitations on the performance intrinsic to linear time invariant (LTI) systems. In this work, we develop a novel control strategy for first order LTI plants with time delay, based on the proportional-integral plus Clegg integrator (PI+CI) controller, a hybrid extension of the proportional-integral (PI) controller, augmented with a new mechanism for keeping its state constant during a given interval of time (reset-and-hold strategy). This strategy is capable of producing an approximation of a flat response which greatly improves the performance in comparison with non-hybrid linear strategies, extending previous results developed for first order systems without delay. Well-posedness and closed-loop stability of the resulting control system are analyzed under the Hybrid Inclusions (HI) framework, and a set of sufficient stability conditions are provided. Furthermore, a case study is developed that showcases the possibilities of this new approach.INDEX TERMS Reset control, hybrid control systems, control design, PI control, nonlinear control systems, time delays.